test/product_syrk.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
// SPDX-License-Identifier: MPL-2.0

#include "main.h"
#include "product_test_helpers.h"

template <typename MatrixType>
void syrk(const MatrixType& m) {
  typedef typename MatrixType::Scalar Scalar;
  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime, RowMajor> RMatrixType;
  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, Dynamic> Rhs1;
  typedef Matrix<Scalar, Dynamic, MatrixType::RowsAtCompileTime> Rhs2;
  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, Dynamic, RowMajor> Rhs3;

  Index rows = m.rows();
  Index cols = m.cols();

  MatrixType m1 = MatrixType::Random(rows, cols), m2 = MatrixType::Random(rows, cols),
             m3 = MatrixType::Random(rows, cols);
  RMatrixType rm2 = MatrixType::Random(rows, cols);

  Rhs1 rhs1 = Rhs1::Random(internal::random<int>(1, 320), cols);
  Rhs1 rhs11 = Rhs1::Random(rhs1.rows(), cols);
  Rhs2 rhs2 = Rhs2::Random(rows, internal::random<int>(1, 320));
  Rhs2 rhs22 = Rhs2::Random(rows, rhs2.cols());
  Rhs3 rhs3 = Rhs3::Random(internal::random<int>(1, 320), rows);

  Scalar s1 = internal::random<Scalar>();

  Index c = internal::random<Index>(0, cols - 1);

  m2.setZero();
  VERIFY_IS_APPROX((m2.template selfadjointView<Lower>().rankUpdate(rhs2, s1)._expression()),
                   ((s1 * rhs2 * rhs2.adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));
  m2.setZero();
  VERIFY(verifyProduct((m2.template triangularView<Lower>() += s1 * rhs2 * rhs22.adjoint()).nestedExpression(),
                       (s1 * rhs2 * rhs22.adjoint()).eval().template triangularView<Lower>().toDenseMatrix(), s1 * rhs2,
                       rhs22.adjoint()));

  m2.setZero();
  VERIFY_IS_APPROX(m2.template selfadjointView<Upper>().rankUpdate(rhs2, s1)._expression(),
                   (s1 * rhs2 * rhs2.adjoint()).eval().template triangularView<Upper>().toDenseMatrix());
  m2.setZero();
  VERIFY(verifyProduct((m2.template triangularView<Upper>() += s1 * rhs22 * rhs2.adjoint()).nestedExpression(),
                       (s1 * rhs22 * rhs2.adjoint()).eval().template triangularView<Upper>().toDenseMatrix(),
                       s1 * rhs22, rhs2.adjoint()));

  m2.setZero();
  VERIFY_IS_APPROX(m2.template selfadjointView<Lower>().rankUpdate(rhs1.adjoint(), s1)._expression(),
                   (s1 * rhs1.adjoint() * rhs1).eval().template triangularView<Lower>().toDenseMatrix());
  m2.setZero();
  VERIFY(verifyProduct((m2.template triangularView<Lower>() += s1 * rhs11.adjoint() * rhs1).nestedExpression(),
                       (s1 * rhs11.adjoint() * rhs1).eval().template triangularView<Lower>().toDenseMatrix(),
                       s1 * rhs11.adjoint(), rhs1));

  m2.setZero();
  VERIFY_IS_APPROX(m2.template selfadjointView<Upper>().rankUpdate(rhs1.adjoint(), s1)._expression(),
                   (s1 * rhs1.adjoint() * rhs1).eval().template triangularView<Upper>().toDenseMatrix());
  VERIFY(verifyProduct((m2.template triangularView<Upper>() = s1 * rhs1.adjoint() * rhs11).nestedExpression(),
                       (s1 * rhs1.adjoint() * rhs11).eval().template triangularView<Upper>().toDenseMatrix(),
                       s1 * rhs1.adjoint(), rhs11));

  m2.setZero();
  VERIFY_IS_APPROX(m2.template selfadjointView<Lower>().rankUpdate(rhs3.adjoint(), s1)._expression(),
                   (s1 * rhs3.adjoint() * rhs3).eval().template triangularView<Lower>().toDenseMatrix());

  m2.setZero();
  VERIFY_IS_APPROX(m2.template selfadjointView<Upper>().rankUpdate(rhs3.adjoint(), s1)._expression(),
                   (s1 * rhs3.adjoint() * rhs3).eval().template triangularView<Upper>().toDenseMatrix());

  m2.setZero();
  VERIFY_IS_APPROX((m2.template selfadjointView<Lower>().rankUpdate(m1.col(c), s1)._expression()),
                   ((s1 * m1.col(c) * m1.col(c).adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));

  m2.setZero();
  VERIFY_IS_APPROX((m2.template selfadjointView<Upper>().rankUpdate(m1.col(c), s1)._expression()),
                   ((s1 * m1.col(c) * m1.col(c).adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));
  rm2.setZero();
  VERIFY_IS_APPROX((rm2.template selfadjointView<Upper>().rankUpdate(m1.col(c), s1)._expression()),
                   ((s1 * m1.col(c) * m1.col(c).adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));
  m2.setZero();
  VERIFY_IS_APPROX((m2.template triangularView<Upper>() += s1 * m3.col(c) * m1.col(c).adjoint()).nestedExpression(),
                   ((s1 * m3.col(c) * m1.col(c).adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));
  rm2.setZero();
  VERIFY_IS_APPROX((rm2.template triangularView<Upper>() += s1 * m1.col(c) * m3.col(c).adjoint()).nestedExpression(),
                   ((s1 * m1.col(c) * m3.col(c).adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));

  m2.setZero();
  VERIFY_IS_APPROX((m2.template selfadjointView<Lower>().rankUpdate(m1.col(c).conjugate(), s1)._expression()),
                   ((s1 * m1.col(c).conjugate() * m1.col(c).conjugate().adjoint())
                        .eval()
                        .template triangularView<Lower>()
                        .toDenseMatrix()));

  m2.setZero();
  VERIFY_IS_APPROX((m2.template selfadjointView<Upper>().rankUpdate(m1.col(c).conjugate(), s1)._expression()),
                   ((s1 * m1.col(c).conjugate() * m1.col(c).conjugate().adjoint())
                        .eval()
                        .template triangularView<Upper>()
                        .toDenseMatrix()));

  m2.setZero();
  VERIFY_IS_APPROX((m2.template selfadjointView<Lower>().rankUpdate(m1.row(c), s1)._expression()),
                   ((s1 * m1.row(c).transpose() * m1.row(c).transpose().adjoint())
                        .eval()
                        .template triangularView<Lower>()
                        .toDenseMatrix()));
  rm2.setZero();
  VERIFY_IS_APPROX((rm2.template selfadjointView<Lower>().rankUpdate(m1.row(c), s1)._expression()),
                   ((s1 * m1.row(c).transpose() * m1.row(c).transpose().adjoint())
                        .eval()
                        .template triangularView<Lower>()
                        .toDenseMatrix()));
  m2.setZero();
  VERIFY_IS_APPROX((m2.template triangularView<Lower>() += s1 * m3.row(c).transpose() * m1.row(c).transpose().adjoint())
                       .nestedExpression(),
                   ((s1 * m3.row(c).transpose() * m1.row(c).transpose().adjoint())
                        .eval()
                        .template triangularView<Lower>()
                        .toDenseMatrix()));
  rm2.setZero();
  VERIFY_IS_APPROX(
      (rm2.template triangularView<Lower>() += s1 * m3.row(c).transpose() * m1.row(c).transpose().adjoint())
          .nestedExpression(),
      ((s1 * m3.row(c).transpose() * m1.row(c).transpose().adjoint())
           .eval()
           .template triangularView<Lower>()
           .toDenseMatrix()));

  m2.setZero();
  VERIFY_IS_APPROX((m2.template selfadjointView<Upper>().rankUpdate(m1.row(c).adjoint(), s1)._expression()),
                   ((s1 * m1.row(c).adjoint() * m1.row(c).adjoint().adjoint())
                        .eval()
                        .template triangularView<Upper>()
                        .toDenseMatrix()));

  // The product of a matrix with itself, rather than with its adjoint, shares its storage without being a rank update.
  m2.setZero();
  m2.template triangularView<Lower>() = m1 * m1;
  VERIFY_IS_APPROX(m2, (m1 * m1).eval().template triangularView<Lower>().toDenseMatrix());
  rm2.setZero();
  rm2.template triangularView<Upper>() += s1 * m1 * m1;
  VERIFY_IS_APPROX(rm2, (s1 * m1 * m1).eval().template triangularView<Upper>().toDenseMatrix());

  // A scalar factor of the update enters twice: (s u) (s u)^* = s conj(s) u u^*.
  {
    const Scalar s2 = internal::random<Scalar>();
    const Rhs2 scaled2 = s2 * rhs2;
    using VectorX = Matrix<Scalar, Dynamic, 1>;
    const VectorX scaledCol = -(s2 * m1.col(c)), conjCol = (s2 * m1.col(c)).conjugate();
    m2.setZero();
    VERIFY_IS_APPROX((m2.template selfadjointView<Lower>().rankUpdate(s2 * rhs2, s1)._expression()),
                     ((s1 * scaled2 * scaled2.adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));
    rm2.setZero();
    VERIFY_IS_APPROX((rm2.template selfadjointView<Upper>().rankUpdate(rhs2 * s2, s1)._expression()),
                     ((s1 * scaled2 * scaled2.adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));
    m2.setZero();
    VERIFY_IS_APPROX((m2.template selfadjointView<Upper>().rankUpdate(-(s2 * m1.col(c)), s1)._expression()),
                     ((s1 * scaledCol * scaledCol.adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));
    rm2.setZero();
    VERIFY_IS_APPROX((rm2.template selfadjointView<Lower>().rankUpdate((s2 * m1.col(c)).conjugate(), s1)._expression()),
                     ((s1 * conjCol * conjCol.adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));
  }

  // destination with a non-default inner-stride
  // see bug 1741
  {
    typedef Matrix<Scalar, Dynamic, Dynamic> MatrixX;
    MatrixX buffer(2 * rows, 2 * cols);
    Map<MatrixType, 0, Stride<Dynamic, 2> > map1(buffer.data(), rows, cols, Stride<Dynamic, 2>(2 * rows, 2));
    buffer.setZero();
    VERIFY_IS_APPROX((map1.template selfadjointView<Lower>().rankUpdate(rhs2, s1)._expression()),
                     ((s1 * rhs2 * rhs2.adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));
    buffer.setZero();
    VERIFY_IS_APPROX(
        (map1.template selfadjointView<Upper>().rankUpdate(rhs2.col(0), s1)._expression()),
        ((s1 * rhs2.col(0) * rhs2.col(0).adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));
    buffer.setZero();
    VERIFY_IS_APPROX(
        (map1.template selfadjointView<Lower>().rankUpdate(rhs2.col(0).transpose(), s1)._expression()),
        ((s1 * rhs2.col(0) * rhs2.col(0).adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));
    buffer.setZero();
    map1.template triangularView<Lower>() = s1 * rhs2.col(0) * rhs22.col(0).adjoint();
    VERIFY_IS_APPROX(
        map1, (s1 * rhs2.col(0) * rhs22.col(0).adjoint()).eval().template triangularView<Lower>().toDenseMatrix());
    VERIFY(buffer.row(1).isZero());
  }

  // outer products into a strictly triangular part
  {
    using VectorX = Matrix<Scalar, Dynamic, 1>;
    VectorX u = VectorX::Random(rows), v = VectorX::Random(rows);
    m2.setZero();
    m2.template triangularView<StrictlyLower>() = s1 * u * v.adjoint();
    VERIFY_IS_APPROX(m2, (s1 * u * v.adjoint()).eval().template triangularView<StrictlyLower>().toDenseMatrix());
    rm2.setZero();
    rm2.template triangularView<StrictlyUpper>() += u * v.adjoint();
    VERIFY_IS_APPROX(rm2, (u * v.adjoint()).eval().template triangularView<StrictlyUpper>().toDenseMatrix());
  }

  // products assigned to a triangular part of a rectangular matrix
  {
    using MatrixX = Matrix<Scalar, Dynamic, Dynamic>;
    MatrixX lhs = MatrixX::Random(rows + 2, 3), rhs = MatrixX::Random(3, rows), tall = MatrixX::Zero(rows + 2, rows);
    tall.template triangularView<Lower>() = lhs * rhs;
    VERIFY_IS_APPROX(tall, (lhs * rhs).eval().template triangularView<Lower>().toDenseMatrix());
    tall.setZero();
    tall.template triangularView<Upper>() += lhs.col(0) * rhs.row(0);
    VERIFY_IS_APPROX(tall, (lhs.col(0) * rhs.row(0)).eval().template triangularView<Upper>().toDenseMatrix());
  }
}

template <typename MatrixType>
void syrk_empty_update(Index size) {
  typedef typename MatrixType::Scalar Scalar;
  typedef Matrix<Scalar, Dynamic, Dynamic> UpdateType;

  MatrixType m = MatrixType::Random(size, size);
  MatrixType ref = m;
  UpdateType empty_update(size, 0);

  m.template selfadjointView<Lower>().rankUpdate(empty_update, Scalar(1));
  VERIFY_IS_APPROX(m, ref);

  m.template selfadjointView<Upper>().rankUpdate(empty_update, Scalar(1));
  VERIFY_IS_APPROX(m, ref);
}

EIGEN_DECLARE_TEST(product_syrk) {
  typedef Matrix<double, Dynamic, Dynamic, RowMajor> RowMajorMatrixXd EIGEN_UNUSED;

  for (int i = 0; i < g_repeat; i++) {
    int s;
    s = internal::random<int>(1, EIGEN_TEST_MAX_SIZE);
    CALL_SUBTEST_1(syrk(MatrixXf(s, s)));
    CALL_SUBTEST_2(syrk(MatrixXd(s, s)));
    TEST_SET_BUT_UNUSED_VARIABLE(s);

    s = internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 2);
    CALL_SUBTEST_3(syrk(MatrixXcf(s, s)));
    CALL_SUBTEST_4(syrk(MatrixXcd(s, s)));
    CALL_SUBTEST_5(syrk(Matrix<bfloat16, Dynamic, Dynamic>(s, s)));
    TEST_SET_BUT_UNUSED_VARIABLE(s);

    CALL_SUBTEST_6(syrk_empty_update<MatrixXd>(48));
    CALL_SUBTEST_7(syrk_empty_update<RowMajorMatrixXd>(48));
  }
}